ERJ Brainteaser: May 2019
19 Sep 2019
This time the top award deservedly goes to one of our most consistent high scorers. And for being to the fore in tackling a particularly tough set of teasers, it is big congratulations to: Industry consultant John Bowen, our new Brainiac of the Month.
What particular feature do the following fractions have in common?
19/95, 26/65, 16/64
Answer: As Jose Padron neatly explained this is a mathematical curiosity, when cancelling the same digit in both denominator and numerator gives the equivalent of the original fraction: 19/95 = 1/5; 26/65 = 2/5; and 16/64 = ¼.
Well done and thanks for your patience, to John Bowen, consultant, Bromsgrove, UK; Jose Padron, material development specialist, Waterville TG Inc., Québec, Canada; John Droogan, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; Hans-Bernd Lüchtefeld, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; and, Yuichi (Joe) Sano, Sumitomo Electric Industries Ltd, Itami, Japan; as well as to Michele Girardi, Scame Mastaf Spa, Suisio, Italy; and Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands, who were on the right track.
Also: Chair challenge
For a live webinar discussion, chairman Dave and his 11 fellow industry experts sit at a round-table. How many ways can the group be arranged, if nobody can sit between two older experts?
With apologies all round, let’s call this teaser null and void: too much confusion and difference in interpretation of the wording. A special thanks to John Droogan here for his help in sorting through this muddle.
For what it’s worth, so, below is the answer to the question, which was sourced from another journal. I should have been wary: they only received one correct answer, and that was from the editor’s brother!
There are 1024 ways, up to rotation around the table. To see this, notice that the youngest journalist must sit right next to Dave – there are two possible places for him. Then, the second youngest journalist must sit right next to this group of two. Once again, there are two possible places for him. Continuing like this, we see that for all journalist except for the oldest one, there are two possible spots on the table. Multiplying two to the power of ten out, we get 1024.
Brian’s bike was sadly stolen from outside his office, so he had to buy a new one. To secure it, he bought two combination locks each having a five-digit code. For the codes, Brian decided to use the smallest and largest numbers that met the following conditions:
1. Each digit of the number was a prime digit.
2. Each successive pair of digits formed a two-digit number that was not a prime number.
3. Each of the prime digits had to appear at least once in the five-digit number.
What were the codes for Brian’s combination locks?
Answer: Someone should tell Brian that his combinations have been rumbled – 32257 and 35772 – though only by a select few of our sharpest readers. Extra well done, so, to: John Bowen, consultant, Bromsgrove, UK; Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; Yuichi (Joe) Sano, Sumitomo Electric Industries Ltd, Itami, Japan; Jose Padron, material development specialist, Waterville TG Inc., Québec, Canada; Ramasubramanian P, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village, Tamil Nadu, India.
On his regular one-mile commute, Brian took three minutes to cycle to work with the wind directly behind him, and returned home in four minutes, cycling against the same wind-force. How long would his journey have taken if there was no wind?
Answer: Okay, a little bit open-to-interpretation regarding whether this was one-way or return journey, but this Brian-teaser really got even our best Brainiacs on their ‘thinking bikes’ – as shown by the two examples further below.
Extra well done, so, to all readers who answered either 3.43 minutes (3min 25.7s) or 6.86 minutes (6 min, 51.4s): John Bowen, consultant, Bromsgrove, UK; Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; Ashley Fahey, sustainability principal vice president, HERO (LGBTQ ERG), Goodyear Tire & Rubber Co., Akron, Ohio, USA; Bharat B Sharma, Sr VP Product Development & Technical Service (Elastomers), Reliance Industries Ltd, Vadodara, Gujarat, India; Ramasubramanian P, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village, Tamil Nadu, India.
Solutions:
John Bowen: With no wind, the time would be 3minutes 25.7seconds.
[Method: Time = distance/speed
Let distance = D, Speed in still air = V and windspeed = W
then With wind speed = V + W, Against wind speed = V – w
Distance is constant, and D = velocity * distabce,
so [V + W]*3 = [V-W]*4, and rearranging, V = 7W, so W = V/7
So with wind, speed = 8V/7, Against wind speed = 6V/7
Time = Distance/Speed, so
3 = D/[8V/7] and 4 = D/[6V-7]
3 = 7D/8V and 4 = 7D/6V
Multiply 3 by 48:
144 = 42D/V
And multiply 4 by 56:
192 = 56D/V
D/V =Time, so when wind is ) and speed is thus V, Time is 144/42 AND 192/56 – both = 3.42857 minutes or 3min 25.7secs]
Jose Padron: Brian would take 6.857 minutes (6 min, 51.4 sec.) would have completed his journey without wind.
Speed with the wind; s+s(wind)=1/3 mile/min
Speed against the wind; s-s(wind)=1/4 mile/min and,
Solving these 2 equation for s we have: 2s=1/3+1/4=7/12
thus: s=7/24 mile/min
The whole journey home-work-home is: 2 miles
and the speed with no wind resistance is: 7/24 mile/min
from the equation: t=d/s=(2*24)/7=48/7=6.875 min.
Elapsed time to complete a journey: 6875 min, = 6min. 51.4 sec.
Fill in the missing years in this tricky millennium sequence:
2307, 2417, 2527, 2637, _, _, _.
Answer: Not so tricky after all, as correct answers quickly arrived in from around the world. The key is that the total from adding the first two digits (eg 27) and last two digits (eg 47) equals the number formed by the middle two digits (eg 74).
2307, 2417, 2527, 2637, 2747, 2857, 2967
Well done in order of arrival to: Amparo Botella, Ismael Quesada SA, Spain; Bharat B Sharma, Sr VP product development & technical service (elastomers), Reliance Industries Ltd, Gujarat, India; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Risto Vettenranta, technical specialist, Ham-Re Oy, Neuvoton, Finland; John Bowen, consultant, Bromsgrove, UK: Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; Ashley Fahey, sustainability principal vice president, HERO (LGBTQ ERG), Goodyear Tire & Rubber Co., Akron, Ohio, USA; Yuichi (Joe) Sano, Sumitomo Electric Industries Ltd, Itami, Japan; Ramasubramanian P, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village, Kanchipuram, Tamil Nadu, India; Hans-Bernd Lüchtefeld, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany.
Using only a total of 3 symbols and without rearranging the numerals, try to get to a total of 100 by placing + (plus) and – (minus) signs between: 1 2 3 4 5 6 7 8 9
Answer: 123 – 45 – 67 + 89 =100
Very well done, in order of reply to: John Droogan, advanced polymers and composites, MegaChem (UK) Ltd, Caldicot, Monmouthshire, UK; Bharat B Sharma, Sr VP product development & technical service (elastomers), Reliance Industries Ltd, Gujarat, India; David Mann, Polymer Business Development, France; John Bowen, consultant, Bromsgrove, UK; Ramasubramanian P, manager, marketing – mixer and LTKMPL products, rubber processing machinery, Larsen & Toubro Ltd, Vedal Village, Kanchipuram, Tamil Nadu, India; Yuichi (Joe) Sano, Sumitomo Electric Industries Ltd, Itami, Japan; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA. Thierry Montcalm, R&D and innovation manager, Soucy Techno, Canada; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; Amparo Botella, Ismael Quesada SA, Spain; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Hans-Bernd Lüchtefeld, market research & communication manager, PHP Fibers GmbH, Obernburg, Germany; Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Lars Linnemann, R&D manager, Genan A/S, Viborg, Denmark
Special mention also to: Bob Hall, Sr. director global marketing, Kraton Polymers LLC, Houston, Texas; Randa Tharwat, import manager, Nacita Automotive, Cairo, Egypt and Salah Younis (no details given) who got there, but by using a couple of extra symbols.
Also thanks to Jose Padron for showing how to work this out using the matrices in this neat table:
